Everyone makes cabinet doors, right? Some of us make more than others. Standard cope-and-stick router or shaper cutters produce nicely mating rail-to-stile joints, but these joints only interpenetrate by about 1/4 in.--hardly enough to create an indestructible joint. And yet, most woodworkers seem to be content with this amount of strength, because there are few alternatives.
In large millwork shops, they customarily mortise the stiles prior to sticking, then they run the rails through a tenoner, which can cope the ends AND produce a sturdy tenon in one pass. In our shop, we mortise the stiles and rails on a converted horizontal milling machine then mold the edges with standard router or shaper cutters. We make tenon stock in long strips, correctly proportioned for the thickness of the frame and the width of the rails--in this case, 3/8-in. thick tenons for 13/16-in. thick doors--then cut the strips into short lengths for the tenons. Usually we rip a very shallow kerf in the faces of the tenon stock to allow air to evacuate during assembly.
This approach is well within the scope of a small hobby shop. To rout the mortises, you can use any type of plunge-router-mortisiing jig that suits you. At American Woodworker, we designed a special "self-centering" mortising jig to hold the work for perfectly centered mortises, but there are plenty of other ways that will work as well, including simple troughs to hold the work in a vise.
Try this method; you'll like it! And you'll never worry about door joints coming loose or breaking if someone bangs into them.